# Exponential Growth and Decay - Concept

###### Explanation

Exponential decay refers to an amount of substance decreasing exponentially. **Exponential decay** is a type of exponential function where instead of having a variable in the base of the function, it is in the exponent. Exponential decay and exponential growth are used in carbon dating and other real-life applications.

###### Transcript

So exponential growth and decay refers

to an amount of substance either

growing or decreasing exponentially.

So what the formula your book is typically

going to be using is this N is equal

to N with this little 0 E to the RT.

What this N is you can either

hear it N 0 or N sub 0.

Either way basically it's

your initial amount.

In general I tend not to be so fond of this

equation because it's just another

equation for me to memorize.

What I want to do is draw some comparisons

how it's exactly the same thing as

our PERT equation which we'll use for

compounded continuously interest.

So basically what we have is N 0 or N sub

0 as our initial amount which corresponds

directly to P which is our principal

or initial amount. We have E to the RT.

Those are exactly the same.

Rate isn't exactly as it was like with a

percent like we want to have interest

that's 4. .04 goes in.

It's a little bit more abstract.

Little bit typically a complicated number but

still a rate that relates to this problem.

T is still time for our exponential growth.

It could vary, be in days, hours, whatever it is.

But it's still just a time.

This term by itself on the left is

going to be the ending amount.

Okay.

So it's another equation but it's really

the exact same thing as PERT which

we already know.

The one other thing we need to talk about

is distinction between exponential

growth and decay.

That's really easy as well.

Exponential growth means something

is getting bigger.

You think of the whole scenario with rabbits

multiplying rapidly, that's exponential

growth.

Okay.

And how that actually pans out is if this

R, this rate is going to be positive,

then our terms are growing.

We're getting bigger.

If this R is negative, then our terms

are going to be getting smaller.

That will be decay.

So exponential growth and decay.

It's a different formula.

But it's really exactly the same as our PERT

formula, just some different letters

thrown in the mix.